A device of this kind for straight cutting in the thread direction of a terry cloth web and where the pile-free sections of the web are utilized for aligning the web is shown in SE-B-437.605 (corresponding to US-A-4,586,411). In order to allow the hemmed longitudinal edges of the web to pass between the alignment rulers at least one of said rulers is provided with recesses. When webs of several different widths occur the alignment rulers must have several such recesses. There is however a certain limitation of the freedom of choice concerning the width of the web with this device.